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If two planes intersect do they intersect in exactly one plane?
No, two planes do not intersect in exactly one plane unless the planes are exactly overlapping, making one plane. In Euclidean Geometry two planes intersect in exactly one line.
Can a given line be in two planes?
Two planes intersect at a line. The line where they intersect pertains to both planes. In the same manner, if infinitely many planes intersect each other at the same line, then that line pertains to the infinitely many planes.
Can two planes intersect in infinitely many points?
yes, it may be the two plane intersect at one line or the two planes are coincident.
Three planes may all intersect each other at exactly one point?
Three planes may all intersect each other at exactly one point. This commonly occurs when there is one straight plane and two other planes intersect it at acute or obtuse angles.
Do two planes intersect in infinitely many points?
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
If two planes intersect do they intersect in exactly one plane?
No, two planes do not intersect in exactly one plane unless the planes are exactly overlapping, making one plane. In Euclidean Geometry two planes intersect in exactly one line.
Do planes intersect in exactly two points?
No. Either they do not intersect at all, or they intersect in a straight line or are the same.
Two planes can intersect on exactly one point?
No, 2 planes may only intersect at a line, a plane, or not at all. THREE planes may intersect at a point though...
Do two distinct planes intersect in a pair of lines?
No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.
What would serve as a counter example to the statement Two planes intersect in exactly one line?
Two planes do not intersect at all if the planes are parallel in three-dimensional space.
Can a given line be in two planes?
Two planes intersect at a line. The line where they intersect pertains to both planes. In the same manner, if infinitely many planes intersect each other at the same line, then that line pertains to the infinitely many planes.
Can two planes intersect in infinitely many points?
yes, it may be the two plane intersect at one line or the two planes are coincident.
Three planes may all intersect each other at exactly one point?
Three planes may all intersect each other at exactly one point. This commonly occurs when there is one straight plane and two other planes intersect it at acute or obtuse angles.
How many different planes may share exactly one point?
None. In conventional geometry, any intersection of two planes defines a line, which is an infinite number of points. Many planes may intersect along a single line, or any pair of planes may intersect creating a unique line, but however they intersect, the number of shared points is infinite. If the the planes do not intersect (if they are parallel), then they share zero points.
Do two planes intersect at a point or a line?
Two planes intersect at a line
Do two planes intersect in infinitely many points?
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
Are there always Two planes intersect in a line?
No. Two planes may be parallel and so may not intersect. Also, any line is the intersection of infinitely many planes, not just two.
